http://codex.wordpress.org/Plugins/Statistics
Read the descriptions and see what your need is.
“Fire Stats” is way cool – delivering a lot of info if you choose. “WP-Shortstas” is a solid simple stat counter that resides in your admin panel.

OK StatCounter requires you to insert its code into a page just before the closing body tag. You don’t do that using the page/post editor. You need to insert the code using the theme editor.
Go to Presentation > theme editor.
Select the file Footer.php and look through to see if it contains the lines
</body>
</html>
If it does insert the statcounter code just before the body tag. Update (save) the file and you should be good to go.